Term Rewriting System R:
[X]
g(X) -> h(X)
c -> d
h(d) -> g(c)

Innermost Termination of R to be shown. 



   R
     ↳Dependency Pair Analysis



R contains the following Dependency Pairs:

G(X) -> H(X)
H(d) -> G(c)
H(d) -> C

Furthermore, R contains one SCC. 


   R
     ↳DPs
       →DP Problem 1
         ↳Rewriting Transformation


Dependency Pairs:

H(d) -> G(c)
G(X) -> H(X)


Rules:


g(X) -> h(X)
c -> d
h(d) -> g(c)


Strategy:

innermost




On this DP problem, a Rewriting SCC transformation can be performed.
As a result of transforming the rule

H(d) -> G(c)
one new Dependency Pair is created:

H(d) -> G(d)

The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Rw
           →DP Problem 2
             ↳Instantiation Transformation


Dependency Pairs:

H(d) -> G(d)
G(X) -> H(X)


Rules:


g(X) -> h(X)
c -> d
h(d) -> g(c)


Strategy:

innermost




On this DP problem, an Instantiation SCC transformation can be performed.
As a result of transforming the rule

G(X) -> H(X)
one new Dependency Pair is created:

G(d) -> H(d)

The transformation is resulting in one new DP problem: 



   R
     ↳DPs
       →DP Problem 1
         ↳Rw
           →DP Problem 2
             ↳Inst
             ...
               →DP Problem 3
                 ↳Remaining Obligation(s)




The following remains to be proven:
Dependency Pairs:

G(d) -> H(d)
H(d) -> G(d)


Rules:


g(X) -> h(X)
c -> d
h(d) -> g(c)


Strategy:

innermost



Innermost Termination of R could not be shown.
Duration:
0:00 minutes